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A framework to perform high‐order deconvolution for finite‐volume method on simplicial meshes
Author(s) -
Bernard Manuel,
Lartigue Ghislain,
Balarac Guillaume,
Moureau Vincent,
Puigt Guillaume
Publication year - 2020
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4839
Subject(s) - polygon mesh , context (archaeology) , curvature , computer science , interpolation (computer graphics) , deconvolution , mathematics , finite volume method , mathematical optimization , smoothness , algorithm , topology (electrical circuits) , geometry , mathematical analysis , artificial intelligence , motion (physics) , paleontology , physics , combinatorics , mechanics , biology
Summary In this article, a new framework to design high‐order approximations in the context of node‐centered finite volumes on simplicial meshes is proposed. The major novelty of this method is that it relies on very simple and compact differential operators, which is a critical point to achieve good performances in the High‐performance computing context. This method is based on deconvolution between nodal and volume‐average values, which can be conducted to any order. The interest of the new method is illustrated through three different applications: mesh‐to‐mesh interpolation, levelset curvature computation, and numerical scheme for convection. Higher order can also be achieved within the present framework by introducing high‐rank tensors. Although these tensors feature much symmetries, their manipulation can quickly become an overwhelming task. For this reason and without loss of generality, the present articles are limited to third‐order expansion. This method, although tightly connected to the k‐exact schemes theory, does not rely on successive corrections: the high‐order property is obtained in a single operation, which makes them more attractive in terms of performances.